Heyward's blast in the seventh inning put the Braves ahead 10-1 and Atlanta also got long balls from Andrelton Simmons (3-for-5, two RBI, three runs scored) and Dan Uggla (three RBI).
Hudson (5-7) posted his first victory since May 5 -- a span of 10 starts -- limiting the Phillies to one run on five hits. The veteran right-hander didn't allow a walk and struck out four.
Kyle Kendrick (7-6) was lit up for six runs on 12 hits over five innings for the Phillies.
Michael Young launched a two-run homer for Philadelphia.